Optimality of the Prym-Tyurin construction for $\mathcal{A}_6$

TL;DR

This paper proves that on a very general principally polarized abelian 6-fold, the minimal algebraic cycle class is a multiple of 6, establishing an optimality result for Prym-Tyurin constructions.

Contribution

It demonstrates the minimal multiple of the minimal curve class that can be represented by an algebraic cycle on such abelian varieties is exactly 6, confirming an optimality aspect.

Findings

The minimal algebraic cycle class on a general abelian 6-fold is 6 times the minimal curve class.

This result confirms the optimality of the Prym-Tyurin construction in this setting.

The proof applies to very general principally polarized abelian 6-folds.

Abstract

We prove that on a very general principally polarized abelian 6-fold, the smallest multiple of the minimal curve class which can be represented by an algebraic cycle is 6.